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MPLAPACK — Multi-Precision Linear Algebra Package

MPLAPACK is a multi-precision linear algebra package based on BLAS and LAPACK, implemented in C++ (C++17 required). It supports a range of high-precision arithmetic libraries including GMP, MPFR, and QD, allowing users to select the backend that best suits their requirements. MPLAPACK is free software distributed under a 2-clause BSD-style license, supplemental to the original LAPACK license.

News

  • 2026-05-12 MPLAPACK 2.2.0 has been released. Available from https://github.com/nakatamaho/mplapack/releases. This final release is based on 2.2.0-rc1: rebased from LAPACK 3.9.1 to 3.12.1, added new BLAS/LAPACK routines including Cgemmtr/Rgemmtr, Cgedmd/Rgedmd, Cgedmdq/Rgedmdq, Cgelst/Rgelst, Clatrs3/Rlatrs3, Cgeqp3rk/Rgeqp3rk, Cunhr_col/Rorhr_col, Cungtsqr_row/Rorgtsqr_row, and Claqz0-4/Rlaqz0-4, and improved robustness across binary80, binary128, DD, QD, GMP, and MPFR. See CHANGES.2.2.0.md. Differences from binary64 behavior and other multiprecision-specific failure modes are summarized in MULTIPRECISION_FAILURE_MODES_2.2.0.md.
  • 2026-04-09 MPLAPACK 2.1.1 released. Patch release: GCC 15 support (external/gmp C23 fix, {C,R}drgvx IPA-modref workaround), arm64 promoted to Tier 1 (Ubuntu arm64 and macOS Apple Silicon), musl/Alpine ARM64 build fix, MinGW laed3 build fix, binary128 std::abs(__float128) ambiguity fix on aarch64-apple-darwin, and a latent DD miscompilation fix (propagating -ffp-contract=off to all DD build targets). OpenBLAS bumped to 0.3.33. ABI/source compatible with 2.1.0.
  • 2026-03-05 MPLAPACK 2.1.0 released. C++17 now required. binary128/binary80 naming unified, MPFR emin/emax auto-adjustment, extended build matrix. LAPACK 3.9.1 Fortran sources are now mechanically converted to idiomatic C++ via Fable and bundled in the release tarball. See CHANGES.2.1.0.md and MIGRATION.md.
  • 2022-09-12 MPLAPACK 2.0.1 released, featuring CUDA versions of Rgemm (dd) and Rsyrk (dd) for Volta and Ampere architectures (~450 GFlops on V100), and Windows DLLs for MinGW-w64.
  • 2022-07-26 MPLAPACK 2.0.0 released. All routines (except mixed-precision) functional and tested across all supported precisions.

Capabilities

  • MPBLAS: All BLAS routines in multiple-precision arithmetic.
  • MPLAPACK: All LAPACK routines in multiple-precision arithmetic (except mixed-precision routines):
    • Linear Equations
    • Linear Least Squares (LLS) Problems
    • Generalized Linear Least Squares (LSE and GLM) Problems
    • Standard Eigenvalue and Singular Value Problems
    • Symmetric Eigenproblems (SEP)
    • Nonsymmetric Eigenproblems (NEP)
    • Singular Value Decomposition (SVD)
    • Generalized Eigenvalue and Singular Value Problems
    • Generalized Symmetric Definite Eigenproblems (GSEP)
    • Generalized Nonsymmetric Eigenproblems (GNEP)
    • Generalized Singular Value Decomposition (GSVD)

Supported Precision Backends

Compiler Support

Compiler binary128 binary80
GCC ✅ Supported ✅ (x86/x86_64 only)
Intel oneAPI (icx/icpx) ✅ Supported ✅ (x86/x86_64 only)
Clang/LLVM ❌ Not supported ✅ Supported

Clang users: binary128 is not supported. Use GCC for binary128. GCC 15: supported as of 2.1.1. On musl-based distros (e.g. Alpine), the binary128 backend stays on __float128 + libquadmath because musl does not ship strfromf128/strfromf64x.

Supported Platforms

Tier Guarantee Platforms
Tier 1 Dedicated release buildtest target; make distcheck + full test suite macOS 15/26 (amd64/arm64), Ubuntu 24.04/26.04 (amd64/arm64), Windows / MinGW-w64 via Ubuntu 24.04/26.04 (amd64), Ubuntu 24.04/26.04 Intel oneAPI (amd64), Debian 12/13 i386
Tier 2 Docker branch build matrix coverage via make tier2; no dedicated release buildtest target Other Debian/Ubuntu architectures and versions, Alpine Linux 3.19–3.23, Rocky Linux 8/9/10, Fedora 42/43, openSUSE Leap 15.6/16.0, openSUSE Tumbleweed
Tier 3 Build-only Docker coverage for selected non-release-gating checks via make tier3; otherwise patches accepted Ubuntu 26.04 amd64 C++ standard variants; other platforms

Release test targets are run from release/. make tier1 runs dedicated remote buildtests; make tier2 runs the Docker branch matrix entries from release/build-matrix.conf; make tier3 runs build-only non-release-gating checks.

Tier Make target OS CPU Host Backend
Tier 1 tier1-macos-arm64 macOS 26 arm64 172.27.109.40 SSH
Tier 1 tier1-macos-amd64 macOS 15 amd64 172.27.109.97 SSH
Tier 1 tier1-ubuntu2404-arm64 Ubuntu 24.04 arm64 172.27.109.40 Docker/Colima
Tier 1 tier1-ubuntu2604-arm64 Ubuntu 26.04 arm64 172.27.109.40 Docker/Colima
Tier 1 tier1-ubuntu2404-amd64 Ubuntu 24.04 amd64 172.27.109.80 Docker
Tier 1 tier1-ubuntu2604-amd64 Ubuntu 26.04 amd64 172.27.109.80 Docker
Tier 1 tier1-ubuntu2404-mingw64-amd64 Windows via Ubuntu 24.04 amd64 172.27.109.80 Docker + MinGW64/Wine
Tier 1 tier1-ubuntu2604-mingw64-amd64 Windows via Ubuntu 26.04 amd64 172.27.109.80 Docker + MinGW64/Wine
Tier 1 tier1-ubuntu2404-inteloneapi-amd64 Ubuntu 24.04 amd64 172.27.109.80 Docker + Intel oneAPI
Tier 1 tier1-ubuntu2604-inteloneapi-amd64 Ubuntu 26.04 amd64 172.27.109.80 Docker + Intel oneAPI
Tier 1 tier1-debian12-i386 Debian 12 i386 172.27.109.80 Docker
Tier 1 tier1-debian13-i386 Debian 13 i386 172.27.109.80 Docker
Tier 3 tier3-ubuntu2604-cxxstd-arm64 Ubuntu 26.04 arm64 172.27.109.40 Docker/Colima build-only
Tier 3 tier3-ubuntu2604-cxxstd-amd64 Ubuntu 26.04 amd64 172.27.109.80 Docker build-only

Dedicated release buildtest scripts are in release/:

release/buildtest_tier1_macos_amd64.sh
release/buildtest_tier1_macos_arm64.sh
release/buildtest_tier1_mingw64_amd64.sh
release/buildtest_tier1_ubuntu_amd64.sh
release/buildtest_tier1_ubuntu_arm64.sh
release/buildtest_tier1_ubuntu_inteloneapi_amd64.sh
release/buildtest_tier1_debian_i386.sh
release/buildtest_tier3_ubuntu2604_cxxstd_arm64.sh
release/buildtest_tier3_ubuntu2604_cxxstd_amd64.sh

How to Build and Install

Prerequisites

  • GCC / G++ / GFortran (C++17 is required; GCC 15 supported as of 2.1.1)
  • wget or curl for release tarball builds, or git for Git checkout builds
  • Standard autotools (autoconf, automake, libtool) are required only when building from a Git checkout
  • ccache is recommended. The misc/reconfig.*.sh helper scripts use it by default.

All third-party libraries (GMP, MPFR, MPC, QD, OpenBLAS, dlfcn-win32) are bundled and built automatically. No separate installation of these libraries is required. For benchmark builds, --with-openblas=system uses the distribution OpenBLAS (-lopenblas) instead of building the bundled OpenBLAS; pass --with-openblas="-L/path -lopenblas" for a custom OpenBLAS location.

Release tarballs already include generated autotools files, so autoreconf is not needed. Git checkout builds must run one of the misc/reconfig.*.sh scripts before make; these scripts generate local build files, run autoreconf, and execute ./configure with the usual MPLAPACK options.

Linux (amd64 / arm64)

Release tarball

mkdir -p $HOME/tmp && cd $HOME/tmp
wget https://github.com/nakatamaho/mplapack/releases/download/v2.1.1/mplapack-2.1.1.tar.xz
tar xvf mplapack-2.1.1.tar.xz
cd mplapack-2.1.1
export CXX=g++ CC=gcc FC=gfortran
./configure \
    --prefix=$HOME/MPLAPACK \
    --enable-gmp=yes \
    --enable-mpfr=yes \
    --enable-binary128=yes \
    --enable-qd=yes \
    --enable-dd=yes \
    --enable-double=yes \
    --enable-test=yes \
    --enable-benchmark=yes
make -j$(nproc)
make install

Git checkout

mkdir -p $HOME/tmp && cd $HOME/tmp
git clone https://github.com/nakatamaho/mplapack.git
cd mplapack
bash misc/reconfig.ubuntu24.04.sh
make -j$(nproc)
make install

For Ubuntu 22.04 or 26.04, use misc/reconfig.ubuntu22.04.sh or misc/reconfig.ubuntu26.04.sh instead. The Linux reconfig scripts enable binary80 automatically on Intel/AMD x86 and omit it on non-x86 CPUs.

To also enable binary80 manually in a tarball build (Intel/AMD x86 only), add --enable-binary80=yes:

./configure \
    --prefix=$HOME/MPLAPACK \
    --enable-binary80=yes \
    --enable-binary128=yes \
    --enable-gmp=yes \
    --enable-mpfr=yes \
    --enable-qd=yes \
    --enable-dd=yes \
    --enable-double=yes \
    --enable-test=yes \
    --enable-benchmark=yes

macOS (Intel or Apple Silicon; using MacPorts)

FSF GCC is required. The default Apple Clang does not support binary128. On Apple Silicon (arm64), omit --enable-binary80=yes (binary80 is x86-only).

Release tarball

sudo port install gcc15 coreutils git gsed
mkdir -p $HOME/tmp && cd $HOME/tmp
wget https://github.com/nakatamaho/mplapack/releases/download/v2.1.1/mplapack-2.1.1.tar.xz
tar xvf mplapack-2.1.1.tar.xz
cd mplapack-2.1.1
export CXX=g++-mp-15 CC=gcc-mp-15 FC=gfortran-mp-15
./configure \
    --prefix=$HOME/MPLAPACK \
    --enable-gmp=yes \
    --enable-mpfr=yes \
    --enable-binary128=yes \
    --enable-qd=yes \
    --enable-dd=yes \
    --enable-double=yes \
    --enable-test=yes \
    --enable-benchmark=yes
# On Intel macs, additionally pass --enable-binary80=yes
make -j$(sysctl -n hw.logicalcpu)
make install

Git checkout

sudo port install gcc15 coreutils git gsed ccache autoconf automake libtool
mkdir -p $HOME/tmp && cd $HOME/tmp
git clone https://github.com/nakatamaho/mplapack.git
cd mplapack
bash misc/reconfig.macOS.sh
make -j$(sysctl -n hw.logicalcpu)
make install

Windows (MinGW-w64 cross-compile on Ubuntu)

Release tarball

sudo apt-get install gcc-mingw-w64-x86-64 g++-mingw-w64-x86-64 gfortran-mingw-w64-x86-64
mkdir -p $HOME/tmp && cd $HOME/tmp
wget https://github.com/nakatamaho/mplapack/releases/download/v2.1.1/mplapack-2.1.1.tar.xz
tar xvf mplapack-2.1.1.tar.xz
cd mplapack-2.1.1
export CXX=x86_64-w64-mingw32-g++
export CC=x86_64-w64-mingw32-gcc
export FC=x86_64-w64-mingw32-gfortran
./configure \
    --host=x86_64-w64-mingw32 \
    --prefix=$HOME/MPLAPACK \
    --enable-gmp=yes \
    --enable-mpfr=yes \
    --enable-binary128=yes \
    --enable-binary80=yes \
    --enable-qd=yes \
    --enable-dd=yes \
    --enable-double=yes \
    --enable-test=yes
make -j$(nproc)
make install

Git checkout

sudo apt-get install git autoconf automake libtool ccache \
    gcc-mingw-w64-x86-64 g++-mingw-w64-x86-64 gfortran-mingw-w64-x86-64
mkdir -p $HOME/tmp && cd $HOME/tmp
git clone https://github.com/nakatamaho/mplapack.git
cd mplapack
bash misc/reconfig.ubuntu24.04.mingw64.sh
make -j$(nproc)
make install

Verifying the Build

make check

Test results are summarized automatically by misc/summarize_mplapack_tests.py.

Experimental CMake Build

MPLAPACK also has an experimental CMake build. The autotools build above remains the primary release path. Unlike autotools, the CMake build does not download or build bundled third-party libraries; GMP, MPFR, MPC, QD, BLAS, and LAPACK are found from the system when the corresponding backends or tests are enabled. See README.cmake.md for the complete option list.

For a dependency-light build that verifies the CMake path itself, build only the double and binary128 backends:

cmake -S . -B build-cmake \
    -DCMAKE_BUILD_TYPE=Release \
    -DMPLAPACK_CXX_STANDARD=23 \
    -DMPLAPACK_CXX_EXTENSIONS=OFF \
    -DMPLAPACK_ENABLE_GMP=OFF \
    -DMPLAPACK_ENABLE_MPFR=OFF \
    -DMPLAPACK_ENABLE_QD=OFF \
    -DMPLAPACK_ENABLE_DD=OFF \
    -DMPLAPACK_ENABLE_DOUBLE=ON \
    -DMPLAPACK_ENABLE_BINARY128=ON \
    -DMPLAPACK_ENABLE_BINARY80=OFF
cmake --build build-cmake -j

On x86/x86_64 systems, add -DMPLAPACK_ENABLE_BINARY80=ON to include the binary80 backend. To run the CMake test targets, enable tests and use CTest:

cmake -S . -B build-cmake \
    -DCMAKE_BUILD_TYPE=Release \
    -DMPLAPACK_BUILD_TESTS=ON
cmake --build build-cmake -j
ctest --test-dir build-cmake --output-on-failure

Install from a CMake build tree with:

cmake --install build-cmake --prefix $HOME/MPLAPACK

Fable — Fortran-to-C++ Conversion Pipeline

Note: The Fable conversion pipeline is not included in the release tarball. It is available only via Git clone. Regenerating sources also requires expanding the bundled LAPACK 3.9.1 source under external/lapack/ before running the scripts.

fable/ is a top-level standalone component providing automated Fortran-to-C++ conversion of LAPACK 3.9.1 sources via Fable and FEM (Fortran Emulator).

# Step 1: clone the repository
git clone https://github.com/nakatamaho/mplapack
cd mplapack

# Step 2: expand bundled LAPACK sources
cd external/lapack
tar xvf lapack-3.9.1.tar.gz
cd ../..

# Step 3: run the conversion pipeline
bash fable/go.sh          # library routines (BLAS/LAPACK C++ sources + headers + patches)
bash fable/go_testing.sh  # test programs (EIG/LIN/MATGEN)

MPLAPACK Test Results

MPLAPACK Benchmark Results

Manual

@misc{2109.13406v2,
  Author = {Maho Nakata},
  Title  = {MPLAPACK version 2.0.1 user manual},
  Year   = {2022},
  Eprint = {arXiv:2109.13406v2},
}

Movies

Slides

MPLAPACK Release Process

MPLAPACK 2.1.1 Release Process

2.1.1 is a patch release. No API/ABI changes vs. 2.1.0. Highlights:

  • GCC 15 support. external/gmp patched for the C23 default (void g(){} → properly typed prototype); patch is gated on GCC >= 15 at configure time. {C,R}drgvx test drivers carry an __attribute__((optimize("O1"))) workaround for a g++-15 IPA-modref miscompilation.
  • arm64 promoted to Tier 1: Ubuntu arm64 and macOS Apple Silicon.
  • musl/Alpine ARM64 build fix (M_PIl fallback).
  • MinGW lapack/laed3 build fix (LAMC3 prototype, max macro guard).
  • binary128 sign() ambiguity on aarch64-apple-darwin / MacPorts GCC 15 fixed (unqualified abs()).
  • DD miscompilation hardening: -ffp-contract=off (and -fp-model strict for icpx) is now propagated to all DD build targets — reference and optimized BLAS/LAPACK, tests, and benchmarks. CUDA DD targets are intentionally excluded (nvcc rejects the flag).
  • configure fix: a stale CXXFLAGS="$SAVE_CXXFLAGS" line was silently clearing user-supplied CXXFLAGS (e.g. -fsanitize=address).
  • std::abs(__float128) probe tightened to require an exact-overload match instead of trusting __SIZEOF_FLOAT128__.
  • dd/qd test comparisons switched from diff to misc/num_diff.py (relative tolerance 1e-30 for dd, 1e-60 for qd) to absorb 1-bit FMA-induced rounding noise.
  • make distcheck fixes: external/openblas/Makefile moved into the benchmark-conditional AC_CONFIG_FILES block; dd/qd test scripts use ${srcdir} for VPATH builds; missing misc/ scripts added to EXTRA_DIST.
  • OpenBLAS updated to 0.3.33 (also fixes the macOS arm64 build).
  • configure build summary: now reports compiler commands and versions, target CPU and integer model, OpenMP runtime, enabled backends, binary128/binary80 type / I/O / math / literal-suffix / interop, and std::abs(__float128) availability.
  • Release build matrix broadened across 77 (OS, arch, toolchain) configurations: Alpine 3.19–3.23, Debian 11–13, Ubuntu 18.04–24.04, Rocky 8–10, Fedora 42/43, openSUSE Leap 15/16, openSUSE Tumbleweed, on x86_64, i386/i686, aarch64, ppc64le, s390x, riscv64, mips64le, plus Intel oneAPI (icpx 2025.3.2) and MinGW-w64 cross targets.
  • Enterprise lifecycle note: Rocky 8/9, openSUSE Leap 15, and Ubuntu 18/20/22 stay on the libquadmath path for their full support window — libquadmath support cannot be dropped yet.

MPLAPACK 2.1.0 Release Process

Tier-S Representative Gate Matrix (Release Blockers)

Tier 1 platforms run the full pipeline including make distcheck. Tier 2 platforms run the Docker branch matrix from release/build-matrix.conf.

# Tier OS Arch Compiler binary80 binary128 Required tasks Date
1 1 macOS Intel Sonoma amd64 GCC (MacPorts) make distcheck + examples -
2 1 macOS Apple Silicon arm64 GCC (MacPorts) N/A make distcheck + examples 2.1.1
3 1 Windows amd64 GCC (MinGW-w64) make distcheck + examples -
4 1 Ubuntu 22.04 amd64 GCC make distcheck + examples -
5 1 Ubuntu 24.04 amd64 GCC make distcheck + examples -
6 1 Ubuntu 24.04 arm64 GCC N/A make distcheck + examples 2.1.1
7 2 Debian 12 i386 GCC N/A build only -
8 2 Rocky 8/9/10 amd64 GCC build only -
9 2 Alpine 3.19–3.23 amd64, arm64, riscv64 GCC ✅ (x86) build only -
10 2 Debian 12/13 ppc64le, s390x, riscv64, mips64le GCC N/A build only -
11 2 Debian 13 amd64 GCC build only -

Tier Policy

Tier 1 (release blockers): make distcheck must pass on all Tier 1 platforms. Tier 2 (matrix coverage): Docker branch build matrix coverage; not release-blocking. Tier 3 (patches accepted): no CI coverage.

CPU Architecture Tiers

Tier Architectures Expectation
1 amd64 (macOS, Windows, Ubuntu); arm64 (macOS, Ubuntu) make distcheck + examples
2 i386, ppc64le, s390x, riscv64, mips64le build only
3 others build-only best-effort

Compiler Tiers

Tier Compilers Expectation
1 GCC 11–15 (native), GCC (MinGW-w64) Must be green
2 Clang Build only; binary128 N/A
Intel oneAPI binary128 and binary80 broken (2024+); oneAPI 2023 worked but no longer readily available; #77

Feature Tiers (Precision)

Tier Feature Primary coverage targets Notes
1 binary80 amd64, i386, Windows (MinGW-w64) N/A on arm64; Clang supported; oneAPI broken
1 binary128 amd64, arm64, macOS (GCC), Windows (MinGW-w64) N/A on Clang; oneAPI broken

MPLAPACK 3.0.0 Release Process

Action Date Status Description
Optimized implementations as default
Add template version mockup: https://github.com/nakatamaho/mplapack-template
Integrate libqd3 and gmpfrxx_mkII Consolidate the next-generation QD and GMP/MPFR C++ wrappers for 3.0.0.
Add OpenBLAS for double benchmark
Update to LAPACK 3.12.1 Patches already bundled in 2.1.0
FMA for QD, DD
Add more benchmarks (Rsyev, Rgesvd, etc.)
Add QA program for BLAS
Take benchmark on A100 (Rgemm, Rsyrk dd)
Python integration
Octave integration
Mixed-precision routines
lp64/ilp64/llp64/ilp32 cleanup
Eliminate compiler warnings
Remove autoreconf/autotools dependency from release tarball builds Tarball users should not need autoconf, automake, libtool, or m4; bundled dependencies should build from shipped configure files.

Old Release Schedules

History

  • 2026-04-09 MPLAPACK 2.1.1 released. GCC 15 support, arm64 promoted to Tier 1 (Ubuntu arm64, macOS Apple Silicon), DD -ffp-contract=off propagation fix, binary128 / MinGW / musl build fixes, OpenBLAS 0.3.33. ABI compatible with 2.1.0.
  • 2026-03-05 MPLAPACK 2.1.0 released. binary128/binary80 naming unified, MPFR emin/emax auto-adjustment, extended build matrix (Alpine, Rocky, Debian i386, CUDA 13.1.1). LAPACK 3.9.1 Fortran sources mechanically converted to idiomatic C++ via Fable and bundled in the release tarball.
  • 2022-09-12 MPLAPACK 2.0.1 released.
  • 2022-07-26 MPLAPACK 2.0.0 released.
  • 2022-06-14 MPLAPACK 2.0.0 alpha released.
  • 2021-11-01 1.0.1 release. Fixed DD and QD arithmetic with Intel oneAPI.
  • 2021-10-01 1.0.0 release. All real LAPACK routines available; SVD and non-symmetric eigenproblem solvers added.
  • 2021-04-11 0.9.3 release. CentOS 7 AArch64 support.
  • 2021-04-01 0.9.0 release. Renamed to mplapack.
  • 2012-12-25 MPACK 0.8.0. NVIDIA C2050 support for Rgemm (double-double).
  • 2010-08-20 MPACK 0.6.7. Condition number estimators added (Rgecon, Rpocon). License changed to 2-clause BSD.
  • 2009-11-24 MPACK 0.6.0.
  • 2008-07-15 mpack-0.0.1. Now configurable and installable.
  • 2008-06-24 Project page created.

Old Page

http://mplapack.sourceforge.net/

Acknowledgment

This work has been supported by: The Special Postdoctoral Researchers' Program of RIKEN (2008, 2009), Grant-in-Aid for Scientific Research (B) 21300017 from the Japan Society for the Promotion of Science (2009–2011), Microsoft Research CORE6 (2010), JSPS KAKENHI Grant no. 18H03206, and TIS inc.

M.N. would like to thank Dr. Imamura Toshiyuki, Dr. Nakasato Naohito, Dr. Fujisawa Katsuki, Dr. Kouya Tomonori, Dr. Takahashi Daisuke, Dr. Goto Kazushige, Dr. Himeno Ryutaro, Dr. Hishimuna Toshiaki, Dr. Katagiri Takahiro, Dr. Ogita Takeshi, Dr. Kashiwagi Masaaki, Dr. Yuasa Fukuko, Dr. Ishikawa Tadashi, Dr. Geshi Masaaki, and Mr. Minato Yuichiro for warm encouragement.

Citation

@misc{2109.13406v2,
  Author = {Maho Nakata},
  Title  = {MPLAPACK version 2.0.1 user manual},
  Year   = {2022},
  Eprint = {arXiv:2109.13406v2},
}

Contact

NAKATA Maho maho.nakata@gmail.com maho@riken.jp

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